Question: Simplify the following expression: $ a = \dfrac{1}{-4q + 7} + 9 $
Solution: In order to add expressions, they must have a common denominator. Multiply the second expression by $\dfrac{-4q + 7}{-4q + 7}$ $ \dfrac{9}{1} \times \dfrac{-4q + 7}{-4q + 7} = \dfrac{-36q + 63}{-4q + 7} $ Therefore $ a = \dfrac{1}{-4q + 7} + \dfrac{-36q + 63}{-4q + 7} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{1 - 36q + 63}{-4q + 7} $ $a = \dfrac{-36q + 64}{-4q + 7}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{36q - 64}{4q - 7}$